Research ArticleNo Access

Threshold dynamics of a nonlocal dispersal SIS epidemic model with free boundaries

Yachun Tong

School of Sciences, Changzhou Institute of Technology, Changzhou 213032, P. R. China

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Inkyung Ahn

Department of Mathematics, Korea University, Sejong 339-700, Republic of Korea

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, and

Zhigui Lin

https://orcid.org/0000-0001-8301-5678

School of Mathematical Science, Yangzhou University, Yangzhou 225002, P. R. China

E-mail Address: zglin@yzu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S179352452350095XCited by:0 (Source: Crossref)

Abstract

To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal susceptible–infected–susceptible (SIS) reaction–diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived. Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities.

Keywords:

AMSC: 35K57, 92D30, 35R35

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